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- Kauffman_polynomial abstract "In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman. It is initially defined on a link diagram aswhere is the writhe of the link diagram and is a polynomial in a and z defined on link diagrams by the following properties:(O is the unknot)L is unchanged under type II and III Reidemeister movesHere is a strand and (resp. ) is the same strand with a right-handed (resp. left-handed) curl added (using a type I Reidemeister move).Additionally L must satisfy Kauffman's skein relation: The pictures represent the L polynomial of the diagrams which differ inside a disc as shown but are identical outside.Kauffman showed that L exists and is a regular isotopy invariant of unoriented links. It follows easily that F is an ambient isotopy invariant of oriented links.The Jones polynomial is a special case of the Kauffman polynomial, as the L polynomial specializes to the bracket polynomial. The Kauffman polynomial is related to Chern-Simons gauge theories for SO(N) in the same way that the HOMFLY polynomial is related to Chern-Simons gauge theories for SU(N) (see Witten's article"Quantum field theory and the Jones polynomial", in Commun. Math. Phys.)".
- Kauffman_polynomial thumbnail Kauffman_poly.png?width=300.
- Kauffman_polynomial wikiPageExternalLink k120040.htm.
- Kauffman_polynomial wikiPageID "9565831".
- Kauffman_polynomial wikiPageRevisionID "561078542".
- Kauffman_polynomial hasPhotoCollection Kauffman_polynomial.
- Kauffman_polynomial subject Category:Knot_theory.
- Kauffman_polynomial subject Category:Polynomials.
- Kauffman_polynomial type Abstraction100002137.
- Kauffman_polynomial type Function113783816.
- Kauffman_polynomial type MathematicalRelation113783581.
- Kauffman_polynomial type Polynomial105861855.
- Kauffman_polynomial type Polynomials.
- Kauffman_polynomial type Relation100031921.
- Kauffman_polynomial comment "In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman. It is initially defined on a link diagram aswhere is the writhe of the link diagram and is a polynomial in a and z defined on link diagrams by the following properties:(O is the unknot)L is unchanged under type II and III Reidemeister movesHere is a strand and (resp. ) is the same strand with a right-handed (resp.".
- Kauffman_polynomial label "Kauffman polynomial".
- Kauffman_polynomial sameAs m.02pk6v8.
- Kauffman_polynomial sameAs Q6378674.
- Kauffman_polynomial sameAs Q6378674.
- Kauffman_polynomial sameAs Kauffman_polynomial.
- Kauffman_polynomial wasDerivedFrom Kauffman_polynomial?oldid=561078542.
- Kauffman_polynomial depiction Kauffman_poly.png.
- Kauffman_polynomial isPrimaryTopicOf Kauffman_polynomial.
